6y^2+13y-25=0

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Solution for 6y^2+13y-25=0 equation:


Simplifying
6y2 + 13y + -25 = 0

Reorder the terms:
-25 + 13y + 6y2 = 0

Solving
-25 + 13y + 6y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-4.166666667 + 2.166666667y + y2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + 2.166666667y + 4.166666667 + y2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + 2.166666667y + y2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + 2.166666667y + y2 = 0 + 4.166666667
2.166666667y + y2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
2.166666667y + y2 = 4.166666667

The y term is 2.166666667y.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667y + 1.173611113 + y2 = 4.166666667 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667y + y2 = 4.166666667 + 1.173611113

Combine like terms: 4.166666667 + 1.173611113 = 5.34027778
1.173611113 + 2.166666667y + y2 = 5.34027778

Factor a perfect square on the left side:
(y + 1.083333334)(y + 1.083333334) = 5.34027778

Calculate the square root of the right side: 2.310904104

Break this problem into two subproblems by setting 
(y + 1.083333334) equal to 2.310904104 and -2.310904104.

Subproblem 1

y + 1.083333334 = 2.310904104 Simplifying y + 1.083333334 = 2.310904104 Reorder the terms: 1.083333334 + y = 2.310904104 Solving 1.083333334 + y = 2.310904104 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + y = 2.310904104 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + y = 2.310904104 + -1.083333334 y = 2.310904104 + -1.083333334 Combine like terms: 2.310904104 + -1.083333334 = 1.22757077 y = 1.22757077 Simplifying y = 1.22757077

Subproblem 2

y + 1.083333334 = -2.310904104 Simplifying y + 1.083333334 = -2.310904104 Reorder the terms: 1.083333334 + y = -2.310904104 Solving 1.083333334 + y = -2.310904104 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + y = -2.310904104 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + y = -2.310904104 + -1.083333334 y = -2.310904104 + -1.083333334 Combine like terms: -2.310904104 + -1.083333334 = -3.394237438 y = -3.394237438 Simplifying y = -3.394237438

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.22757077, -3.394237438}

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